RICHARD J. HARRIS

Examples spanning 20 years and various areas of social psychology illustrate the great difficulty of knowing what implications do or do not follow from the postulates of verbally stated theories. Reliance on verbally stated theories in preference to mathematical or computer-simulation models thus severs a vital link in the hypothetico-deductive chain.

The goal of this paper is to illustrate the great difficulty of knowing what research hypotheses do or do not follow from the postulates of any but the simplest, single-factor verbally stated theory. Convincing evidence would be provided by a comprehensive survey of all verbally stated theories subjected to empirical test in, say, the past 10 years, with a sufficiently detailed analysis of each to demonstrate its inherent ambiguity. The less comprehensive approach taken in thc present paper is to provide this sort of analysis for a few examples of research hypotheses widely accepted as following from well-known theories, in hopes that the existence of ambiguities in even these cases, despite the credentials of the theories, theorists, and researchers involved, will convince the reader that the problem is not restricted to neophytes or incompetents.

Specifically, we will focus upon theories that embody sufficiently perceptive insights to have stimulated wide interest and that are considerably above average in the care and precision with which their authors have stated their postulates. These theorists, by the very excellence of their efforts, carry a disproportionate responsibility for the widespread impression among social psychologists that the precision and testability of mathematical models can be achieved (with less algebraic labor and no loss of audience) by carefully stated verbal theories. In seeking to dispel this notion, the present paper must take on a predominantly negative tone. Excellent discussions of the positive virtues of formal models are available elsewhere (e.g., Abelson, 1968; Atkinson, Bower, & Crothers, 1965; Estes, 1957; Rosenberg, 1968).

Each example offered below will present the verbal postulates of a theory, together with one or more verbally stated) research hypotheses "derived" from these postulates. A translation of the postulates into mathematical symbols and equations will then be offered, and it will be shown that the research hypotheses do not necessarily follow from the postulates of the theory. The particular mathematical translation offered for any given verbal theory is only one (and not necessarily the best) of many possible translations, each consistent with the verbally stated postulates. One such translation is sufficient for present purposes, however, since a claim that some hypothesis "follows from" or "is derived from" a set of postulates is equivalent to the claim that this hypothesis would follow from any reasonable translation of those postulates. This is best illustrated by considering our first example.

Please send reprint requests to R. J. Harris, Department of Psychology, University of New Mexico, Albuquerque, New Mexico 87131. The final draft of this paper-was prepared while the author was Visiting Associate Professor in the Department of Psychology, Ohio State University. A more caustic version of the present paper is available in Harris (Note 1), which paper was the basis of a presentation by the same title at the 82nd annual convention of the American Psychological Association in New Orleans, September 2. 1974, a three-page abstract of which was published in the Division 8 proceedings of that convention (Personality and Social Psychology Bulletin, 1974, 1, 1-3).

Festinger’s (1954) theory of social comparison processes includes "Derivation D₁: When a discrepancy exists with respect to opinions or abilities there will be tendencies to change one’s own position so as to move closer to others in the group" (p.126). Im addition, social comparison theory includes "Hypothesis IV: There is a unidirectional drive upward in the case of abilities which is largely absent in opinions" (p. 124). From a consideration of the interaction of these two factors, Festinger concludes that "When and if uniformity of opinion is achieved, there is a state of social quiescence" (p. 125). but that for abilities "a state of social quiescence is never reached" (p. 125) because each individual wishes "to be slightly better than the others with whom (he) compares (himself)" (p. 127), and this goal cannot be achieved simultaneously by all members of the group.

On the surface, this contention would seem to contradict Derivation D₁, since being slightly better than comparison persons would represent a (small) discrepancy with respect to abilities which Derivation D₁ claims one will attempt to reduce. However, we can assume that Festinger meant to say "When a sufficiently large discrepancy exists..." and/or that Derivation D₁ and Hypothesis IV represent separate forces which summate in determining the point at which net pressure to change is zero. A more formal representation of this portion of social comparison theory is provided by the statement that each member of a group will seek to adjust his position on the ability dimension so as to maximize D(x), the desirability of his position x, where D(x)= c(x) – u(x), c(x) being the comparison-based component of the desirability of position x and u(x) being the component attributable to the unidirectional drive upward. The verbal statements of social comparison theory further imply that c(x) must be a monotonically decreasing function of ½ x - x_other½ , (the absolute value, sign ignored, of the difference between x and thc position on the ability dimension of a comparison person), while u(x) must be some monotonically decreasing function of x. The research hypothesis Festinger "derived" from social comparison theory and for which he provided evidence based on studies of level of aspiration and of intra-group competition amounts to the assertion that D(x) attains its maximum for a value of x slightly higher than x_other. Unfortunately, this research hypothesis does not necessarily follow from social comparison theory.

It can readily be shown that the maximum value of D(x) cannot be attained for any value of x < x_other However, the maximum may occur for x º x_other (x identically equal to x_other), thus obliterating the claimed distinction between opinions and abilities, or for x arbitrarily large. For instance, if u(x) = ax and c(x) = ½ x_other½ , then the maximum value of D(x) occurs for x º x_other if a < 1, (i.e., if comparison is a more important motive than improvement), but for x = +∞ if a < 1. If, on thc other hand, u(x) = x" and c(x) = -(x- x_other) ², then if a > 2, D(x) attains its maximum value at x = +∞. Also, if, u(x) = (x)^1/2 and c(x) = -e½ ^{x - x}other½ , then D(x) is maximized at x º x_other.

There are choices of u(x) and c(x)--for example, u(x) = x^1/2 and -(x- x_other)²--, from which the research hypothesis does follow. However, the verbal postulates of social comparison theory require nothing of the functions u(x) and c(x) beyond monotonicity, so that Festinger's claim that this hypothesis follows from social comparison theory is incorrect. Thus data supportive of the research hypothesis (e.g., Hakmiller, 1966, p. 53) are irrelevant to an evaluation of social comparison theory as stated by Festinger (1954).

Brehm and Cohen (1963) offer the following "derivation" from the theory of cognitive dissonance:

These statements read quite smoothly, and produce a compelling feeling of agreement with the "derivation" in the second quoted paragraph. Certainly Greenwald (1969), in attempting to test this derivation, was under the impression that it follows from the assumptions of dissonance theory. It does not.

Consider the four kinds of cognitive elements involved in the post-decision spread paradigm. Considering the special case of equally important cognitions, the statements in the first paragraph of the quote "translate" into d = f_mi[(n_-c +n_+r)/(n_+c +n_-r)], where d = magnitude of dissonance; n_+c, n_-c, etc., represent the number of positive and negative features of the chosen (c) and rejected (r) alternatives; and f_mi(y) represents any monotonically increasing function of y.

Brehm and Cohen provide no definition of "relative attractiveness" (a_r.) or of total attractiveness (a_t, "the more attractive they both are"). Greenwald (1969), however, employed difference in ratings as the operational definition of a_r, suggesting that a difference-based conceptual definition might be in order, such as a_r = (n_+c + n_-r) - (n_-c + n_+r); whence (n_-c + n_+r) = (n_+c + n_-r) – a_r.. Incorporating this definition into our earlier definition of d yields

d = f_mi[(n_+c + n_-r – a_r)/(n_+c + n_-r)] = f_mi[1 – a_r/(n_+c + n_-r)] (1)

It also seems compelling that we should, in this context, define "total attractiveness" as

a_t = (n_+c + n_+r) – (n_-c + n_-r).

Let us now consider three possible ways of increasing a_t while holding a_r constant:

(i) Increase both n_+c and n_+r by the same amount. This clearly holds a_r constant while n_+c increases, thus increasing d.

(ii) Decrease both n_-c and n_-r by the same amount. Thus, in Eq. (1), a_r and n_+c are held constant while n_-r, decreases, thus decreasing d.

(iii) Increase n_+c. and decrease n_-r by the same amount. This leads to no change either in a_r or in (n_+c + n_-r), and thus no change in d.

Thus, if a difference definition of relative attractiveness is adopted, dissonance theory predicts that increasing the total attractiveness of the two alternatives may increase, decrease, or leave unchanged the magnitude of the resulting dissonance, depending on exactly how total attractiveness is increased while maintaining constant relative attractiveness. This prediction of a strong interaction between the method of altering a_t and the magnitude of the resulting postdecision spread effect could provide the basis for an interesting empirical study. However, Greenwald (1969) was under the impression that Brehm and Cohen's (1963) "derivation" of a simpler relationship was valid. He thus neither manipulated nor measured these finer details (n_+c, n_-r, etc.) of the differences among his alternatives, and interpreted the U-shaped relationship he obtained between d and a_t as inconsistent with dissonance theory.

Gerard (1964, 1965) applied dissonance theory to Asch's (1956) line-judgment conformity paradigm, concluding that the subject's public agreement or disagreement with the false majority on one trial should establish strong pressure to repeat this conforming or nonconforming response on subsequent trials. Gerard then claimed that this "commitment effect" implied that the frequency distribution, across subjects, of number of conforming responses should be bimodal in a face-to-face, two-alternative situation, and described data that he claimed supported this derivation. Unfortunately, (i) Gerard’s assumptions do not necessarily imply bimodality; (ii) Gerard’s data do not necessarily display bimodality; and (iii) bimodality could arise in the absence of a commitment effect.

With respect to the first point: one reasonable representation of a commitment effect would be to assume that Pr(C_n+1/C_n)= a and Pr(N_n+1/N_n) = b, where C_n represents the event "S conforms to the false majority on trial n," N_n represents the event "S doesn't conform on trial n," and a and b are each constants independent of n and greater than one-half. Kiesler and Kiesler (1969) interpreted Gerard's verbal statements as implying (translating to the present symbols) that a = b = 1.0. This not only implies bimodality, but a two-point frequency distribution with all subjects emitting either 0 or 100% conforming responses. Neither Gerard nor any other researcher has obtained such a complete absence of intermediate frequencies.³

We need not hold Gerard himself to unity values of a and b, as he includes qualifiers such as "not irrevocably" and "will tend to" in both papers. Does the more general model necessarily imply bimodality? Taking the simple case where there are only four false-majority trials in the experiment, Table 1 gives the theoretical expressions and specific numerical examples for the frequency distribution of number of conforming responses. (Note that we have had to add as a parameter p₁, the probability of a conforming response on the first trial, before any commitment effect is operative.)

As the examples in Table 1 show, Gerard's assumptions may imply (i) a symmetric, unimodal distribution; (ii) a symmetric, bimodal. U-shaped distribution; or (iii) a monotonically decreasing distribution. (They can also generate a monotonic increasing distribution if p₁ is much greater than .5, but this seems unlikely.)

Predicted frequency distribution of number of conforming responses^α

α The entries in this table were obtained by the "brute force" method of multiplying trial-to-trial conditional probabilities for each of the 16 possiblc sequences and then summing together the probabilities of all sequences involving a given number of conforming responses (errors). For instance, Pr(1 error) = Pr(C₁) • Pr(N₂/C₁) • Pr(N₃/N₂) • Pr(N₁/N₃) + Pr(N₁) • Pr(C₂/N₁) • Pr(N₃/C₂) • Pr(N₄/N₃) + Pr(N₁) • Pr(N₂/N₁) • Pr(C₃/N₂) • Pr(N₁/C₃) + Pr(N₁) • Pr(N₂/N₁) • Pr(N₃/N₂) • Pr(C₄/N₃) = p₁(1 - a)b² + (1 - p₁)(1 – b)(1 – a)b + (1 – p₁)b(1 – b)(1 – a) + (1 – p₁)b²(1 – b).

It is not clear whether Gerard's data actually display bimodality. The papers present only grouped frequency distributions with very unequal interval sizes. For instance, Gerard (1964) reports that in his face-to-face conditions nine subjects made 0 errors, 11 made from one to four errors, and the remaining 18 subjects made from five to 24 conforming responses. These data could have arisen from a bimodal distribution. They could also arise, however, from a monotonically decreasing function much like the right-hand column of Table 1, since they represent averages of 9 subjects per cell for k = 0, 2.75 subjects per cell for k = 1 through k = 4, and 0.9 subjects per cell for k = 5 through k = 24.

Gerard's distribution is also consistent with an individual-differences model involving no commitment effect whatever. For instance, we could assume that nine of the subjects were unconditional nonconformists, while the remaining 29 subjects conformed with a fixed probability of .2165. Thus, Gerard's dissonance-theoretic analysis neither implies nor is implied by his data.

The formal representation of Gerard's theory offered here could form the basis of a series of studies investigating the effects of individual or group differences in "base rate" of conformity (p₁) and in the strength of commitment effects (a and b). Such analyses would be greatly strengthened by focusing on the sequential features of the data. Cohen (1963) has performed such studies and analyses, concluding that no two-state model such as the one offered here can account both for the early "vacillation" and for the subsequent "absorption" into consistent conformity or consistent nonconformity which are typically found in the Asch paradigm. Cohen was rather successful in accounting for both these features by positing a four-state (permanent conformity, temporary conformity, temporary nonconformity, and permanent nonconformity) Markov chain.

Larsen, Schwendiman, and Stimpson (1968) argued that contact with minority groups should be more effective in changing attitudes toward that group if the observed behavior is incongruent with the observer's stereotype of that group. These authors had a black confederate behave (during a videotaped interview) either in a manner which reinforced positive stereotypes of blacks (positive interview) or in a way which reinforced negative views of blacks. They found the changes reported in Table 2 in general stereotypes toward blacks (on a scale ranging from -22 to +22) on the part of persons holding initially positive or initially negative attitudes.

TABLE 2

Changes in general stereotypes toward Blacks^α

The authors cite these data as supportive of their hypothesis. However, this analysis implicitly assumes the additive model of attitude change, namely that X_new = X_old + c, where c = X_new - X_old represents the effect and │c │, the effectiveness of the communication. If we assume instead Anderson's (1959) proportional-change model of attitude change, namely, that X_new = X_old + θ(X_adv – S_old), where X_adv is thc position advocated by the communication and θ represents its effectiveness, we find that we can perfectly reproduce Larsen et al.'s results by assuming that X_adv was 20.58 for the positive interview, and its effectiveness (θ) was .303 for all subjects, irrespective of initial attitude; while the negative interview had an X_adv of -13.25 and a θ of .119 for all subjects. These are quite reasonable parameter values, since we might expect it to be more difficult to select extremely negative behaviors than strongly positive behaviors to include inan interview "script" (whence X_adv is greater for the positive than the negative interview), and we might expect any but a very skilled actor to find it easier to “get into” a role involving positive self-presentation than to convincingly portray himself as despicable (whence θ₊ > θ_-).

The validity of this alternative analysis cannot be tested in the absence of data on X_adv for the two interviews. It is nevertheless interesting that assuming θ to be affected only by congruity or only by the initial attitude of the subject and then solving for values of X_adv and θ consistent with the obtained means requires off-scale estimates of X_adv = +78.5 and +34.5, respectively, for the positive interview. The main point is that the results are ambiguous unless some theoretical commitment to a particular attitude change model is made and data sufficient to test that model are collected. The modus operandi in attitude research, however, seems to be to use the additive model (because of its convenience) if simple change measures support the researcher’s predictions, throwing in percentage of change measures (θs) only if necessary to make one’s predictions come out right.⁴

Numerous other examples could be given. For instance, the literature of the social sciences over the past two centuries is replete with references to "group utility functions" or to "the greatest good for the greatest number." Yet Arrow (1951), beginning with a few, intuitively compelling criteria for a group decision procedure (transitivity, responsiveness, independence of irrelevant alternatives) showed that no such procedure could be devised which was not either imposed (thus leading to preordained decisions which were completely independent of thc preferences of the group members) or dictatorial (i.e., determined completely by the preferences of a single group member).

More recently, Harris (1976) pointed out that equity theorists have tested a number of hypotheses (e.g., that denigrating a victim's inputs can be used to restore equity) which did not necessarily follow from their definitions of equity.

Hopefully those examples will suffice to convince the reader that reliance on verbal theories severs a vital link in the cycle from theory to derivation to empirical test to revised theory which constitutes the scientific method. This is not to deny the usefulness of the facts established in the process of testing any hypothesis, no matter what its source, nor that research hypotheses inspired by (if not actually derived from) verbal theories may be especially useful. However. progress toward theory development and testing wilt be impeded if we continue to treat our intuitions about the implications of verbally stated postulates as if they had the same reliability and testability as mathematical derivations from formally stated theories.

(Received January 3. 1975)